This paper attempts firstly to derive a mathematical model of the dynamics of a set of dual fingers with soft and deformable tips which grasps and manipulates a rigid object with some dexterity. To gain a physical insight into the problem, consideration is restricted to the case that the motion of the whole system is confined to a horizontal plane. Secondly on the basis of the derived model it is shown that the rotation of the object can be indirectly controlled by the change of positions of the center points of both contact areas on the object. Then, each of the center points of contact areas can be positioned by inclining the last link of each corresponding finger against the object. It is further shown that, when both forces of pressing the object becomes almost equal, the equation of motion of the object in terms of rotational angles assumes the form of a harmonic oscillator with a forcing term, which can be regulated coordinately by the relative angle between the two last links contacting with the object. It is also shown that dynamics of this system satisfy passivity. Finally, design problems of control for dynamic stable grasping and enhancing dexterity in manipulating things are discussed on the basis of passivity analysis.

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This paper is concerned with the design of a state feedback control scheme for variable stiffness actuated (VSA) robots, which guarantees prescribed performance of the tracking errors despite the low range of mechanical stiffness. The controller does not assume knowledge of the actual system dynamics nor does it utilize approximating structures (e.g., neural networks and fuzzy systems) to acquire such knowledge, leading to a low complexity design. Simulation studies, incorporating a model validated on data from an actual variable stiffness actuator (VSA) at a multi-degrees-of-freedom robot, are performed. Comparison with a gain scheduling solution reveals the superiority of the proposed scheme with respect to performance and robustness.Index Terms-Flexible joint robot control, nonlinear control, prescribed performance control (PPC), robust robot control, uncertain systems, variable stiffness actuators (VSAs).

In this paper, we address unresolved issues in robot force/position tracking including the concurrent satisfaction of contact maintenance, lack of overshoot, desired speed of response, as well as accuracy level. The control objective is satisfied under uncertainties in the force deformation model and disturbances acting at the joints. The unknown nonlinearities that arise owing to the uncertainties in the force deformation model are approximated by a neural network linear in the weights and it is proven that the neural network approximation holds for all time irrespective of the magnitude of the modeling error, the disturbances, and the controller gains. Thus, the controller gains are easily selected, and potentially large neural network approximation errors as well as disturbances can be tolerated. Simulation results on a 6-DOF robot confirm the theoretical findings.

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